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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.special;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.OutOfRangeException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.util.ContinuedFraction;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.22"></a>
<FONT color="green">023</FONT>    <a name="line.23"></a>
<FONT color="green">024</FONT>    /**<a name="line.24"></a>
<FONT color="green">025</FONT>     * &lt;p&gt;<a name="line.25"></a>
<FONT color="green">026</FONT>     * This is a utility class that provides computation methods related to the<a name="line.26"></a>
<FONT color="green">027</FONT>     * Beta family of functions.<a name="line.27"></a>
<FONT color="green">028</FONT>     * &lt;/p&gt;<a name="line.28"></a>
<FONT color="green">029</FONT>     * &lt;p&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     * Implementation of {@link #logBeta(double, double)} is based on the<a name="line.30"></a>
<FONT color="green">031</FONT>     * algorithms described in<a name="line.31"></a>
<FONT color="green">032</FONT>     * &lt;ul&gt;<a name="line.32"></a>
<FONT color="green">033</FONT>     * &lt;li&gt;&lt;a href="http://dx.doi.org/10.1145/22721.23109"&gt;Didonato and Morris<a name="line.33"></a>
<FONT color="green">034</FONT>     *     (1986)&lt;/a&gt;, &lt;em&gt;Computation of the Incomplete Gamma Function Ratios<a name="line.34"></a>
<FONT color="green">035</FONT>     *     and their Inverse&lt;/em&gt;, TOMS 12(4), 377-393,&lt;/li&gt;<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;li&gt;&lt;a href="http://dx.doi.org/10.1145/131766.131776"&gt;Didonato and Morris<a name="line.36"></a>
<FONT color="green">037</FONT>     *     (1992)&lt;/a&gt;, &lt;em&gt;Algorithm 708: Significant Digit Computation of the<a name="line.37"></a>
<FONT color="green">038</FONT>     *     Incomplete Beta Function Ratios&lt;/em&gt;, TOMS 18(3), 360-373,&lt;/li&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     * &lt;/ul&gt;<a name="line.39"></a>
<FONT color="green">040</FONT>     * and implemented in the<a name="line.40"></a>
<FONT color="green">041</FONT>     * &lt;a href="http://www.dtic.mil/docs/citations/ADA476840"&gt;NSWC Library of Mathematical Functions&lt;/a&gt;,<a name="line.41"></a>
<FONT color="green">042</FONT>     * available<a name="line.42"></a>
<FONT color="green">043</FONT>     * &lt;a href="http://www.ualberta.ca/CNS/RESEARCH/Software/NumericalNSWC/site.html"&gt;here&lt;/a&gt;.<a name="line.43"></a>
<FONT color="green">044</FONT>     * This library is "approved for public release", and the<a name="line.44"></a>
<FONT color="green">045</FONT>     * &lt;a href="http://www.dtic.mil/dtic/pdf/announcements/CopyrightGuidance.pdf"&gt;Copyright guidance&lt;/a&gt;<a name="line.45"></a>
<FONT color="green">046</FONT>     * indicates that unless otherwise stated in the code, all FORTRAN functions in<a name="line.46"></a>
<FONT color="green">047</FONT>     * this library are license free. Since no such notice appears in the code these<a name="line.47"></a>
<FONT color="green">048</FONT>     * functions can safely be ported to Commons-Math.<a name="line.48"></a>
<FONT color="green">049</FONT>     * &lt;/p&gt;<a name="line.49"></a>
<FONT color="green">050</FONT>     *<a name="line.50"></a>
<FONT color="green">051</FONT>     *<a name="line.51"></a>
<FONT color="green">052</FONT>     * @version $Id: Beta.java 1420669 2012-12-12 13:40:35Z erans $<a name="line.52"></a>
<FONT color="green">053</FONT>     */<a name="line.53"></a>
<FONT color="green">054</FONT>    public class Beta {<a name="line.54"></a>
<FONT color="green">055</FONT>        /** Maximum allowed numerical error. */<a name="line.55"></a>
<FONT color="green">056</FONT>        private static final double DEFAULT_EPSILON = 1E-14;<a name="line.56"></a>
<FONT color="green">057</FONT>    <a name="line.57"></a>
<FONT color="green">058</FONT>        /** The constant value of ½log 2π. */<a name="line.58"></a>
<FONT color="green">059</FONT>        private static final double HALF_LOG_TWO_PI = .9189385332046727;<a name="line.59"></a>
<FONT color="green">060</FONT>    <a name="line.60"></a>
<FONT color="green">061</FONT>        /**<a name="line.61"></a>
<FONT color="green">062</FONT>         * &lt;p&gt;<a name="line.62"></a>
<FONT color="green">063</FONT>         * The coefficients of the series expansion of the Δ function. This function<a name="line.63"></a>
<FONT color="green">064</FONT>         * is defined as follows<a name="line.64"></a>
<FONT color="green">065</FONT>         * &lt;/p&gt;<a name="line.65"></a>
<FONT color="green">066</FONT>         * &lt;center&gt;Δ(x) = log Γ(x) - (x - 0.5) log a + a - 0.5 log 2π,&lt;/center&gt;<a name="line.66"></a>
<FONT color="green">067</FONT>         * &lt;p&gt;<a name="line.67"></a>
<FONT color="green">068</FONT>         * see equation (23) in Didonato and Morris (1992). The series expansion,<a name="line.68"></a>
<FONT color="green">069</FONT>         * which applies for x ≥ 10, reads<a name="line.69"></a>
<FONT color="green">070</FONT>         * &lt;/p&gt;<a name="line.70"></a>
<FONT color="green">071</FONT>         * &lt;pre&gt;<a name="line.71"></a>
<FONT color="green">072</FONT>         *                 14<a name="line.72"></a>
<FONT color="green">073</FONT>         *                ====<a name="line.73"></a>
<FONT color="green">074</FONT>         *             1  \                2 n<a name="line.74"></a>
<FONT color="green">075</FONT>         *     Δ(x) = ---  &gt;    d  (10 / x)<a name="line.75"></a>
<FONT color="green">076</FONT>         *             x  /      n<a name="line.76"></a>
<FONT color="green">077</FONT>         *                ====<a name="line.77"></a>
<FONT color="green">078</FONT>         *                n = 0<a name="line.78"></a>
<FONT color="green">079</FONT>         * &lt;pre&gt;<a name="line.79"></a>
<FONT color="green">080</FONT>         */<a name="line.80"></a>
<FONT color="green">081</FONT>        private static final double[] DELTA = {<a name="line.81"></a>
<FONT color="green">082</FONT>            .833333333333333333333333333333E-01,<a name="line.82"></a>
<FONT color="green">083</FONT>            -.277777777777777777777777752282E-04,<a name="line.83"></a>
<FONT color="green">084</FONT>            .793650793650793650791732130419E-07,<a name="line.84"></a>
<FONT color="green">085</FONT>            -.595238095238095232389839236182E-09,<a name="line.85"></a>
<FONT color="green">086</FONT>            .841750841750832853294451671990E-11,<a name="line.86"></a>
<FONT color="green">087</FONT>            -.191752691751854612334149171243E-12,<a name="line.87"></a>
<FONT color="green">088</FONT>            .641025640510325475730918472625E-14,<a name="line.88"></a>
<FONT color="green">089</FONT>            -.295506514125338232839867823991E-15,<a name="line.89"></a>
<FONT color="green">090</FONT>            .179643716359402238723287696452E-16,<a name="line.90"></a>
<FONT color="green">091</FONT>            -.139228964661627791231203060395E-17,<a name="line.91"></a>
<FONT color="green">092</FONT>            .133802855014020915603275339093E-18,<a name="line.92"></a>
<FONT color="green">093</FONT>            -.154246009867966094273710216533E-19,<a name="line.93"></a>
<FONT color="green">094</FONT>            .197701992980957427278370133333E-20,<a name="line.94"></a>
<FONT color="green">095</FONT>            -.234065664793997056856992426667E-21,<a name="line.95"></a>
<FONT color="green">096</FONT>            .171348014966398575409015466667E-22<a name="line.96"></a>
<FONT color="green">097</FONT>        };<a name="line.97"></a>
<FONT color="green">098</FONT>    <a name="line.98"></a>
<FONT color="green">099</FONT>        /**<a name="line.99"></a>
<FONT color="green">100</FONT>         * Default constructor.  Prohibit instantiation.<a name="line.100"></a>
<FONT color="green">101</FONT>         */<a name="line.101"></a>
<FONT color="green">102</FONT>        private Beta() {}<a name="line.102"></a>
<FONT color="green">103</FONT>    <a name="line.103"></a>
<FONT color="green">104</FONT>        /**<a name="line.104"></a>
<FONT color="green">105</FONT>         * Returns the<a name="line.105"></a>
<FONT color="green">106</FONT>         * &lt;a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"&gt;<a name="line.106"></a>
<FONT color="green">107</FONT>         * regularized beta function&lt;/a&gt; I(x, a, b).<a name="line.107"></a>
<FONT color="green">108</FONT>         *<a name="line.108"></a>
<FONT color="green">109</FONT>         * @param x Value.<a name="line.109"></a>
<FONT color="green">110</FONT>         * @param a Parameter {@code a}.<a name="line.110"></a>
<FONT color="green">111</FONT>         * @param b Parameter {@code b}.<a name="line.111"></a>
<FONT color="green">112</FONT>         * @return the regularized beta function I(x, a, b).<a name="line.112"></a>
<FONT color="green">113</FONT>         * @throws org.apache.commons.math3.exception.MaxCountExceededException<a name="line.113"></a>
<FONT color="green">114</FONT>         * if the algorithm fails to converge.<a name="line.114"></a>
<FONT color="green">115</FONT>         */<a name="line.115"></a>
<FONT color="green">116</FONT>        public static double regularizedBeta(double x, double a, double b) {<a name="line.116"></a>
<FONT color="green">117</FONT>            return regularizedBeta(x, a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);<a name="line.117"></a>
<FONT color="green">118</FONT>        }<a name="line.118"></a>
<FONT color="green">119</FONT>    <a name="line.119"></a>
<FONT color="green">120</FONT>        /**<a name="line.120"></a>
<FONT color="green">121</FONT>         * Returns the<a name="line.121"></a>
<FONT color="green">122</FONT>         * &lt;a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"&gt;<a name="line.122"></a>
<FONT color="green">123</FONT>         * regularized beta function&lt;/a&gt; I(x, a, b).<a name="line.123"></a>
<FONT color="green">124</FONT>         *<a name="line.124"></a>
<FONT color="green">125</FONT>         * @param x Value.<a name="line.125"></a>
<FONT color="green">126</FONT>         * @param a Parameter {@code a}.<a name="line.126"></a>
<FONT color="green">127</FONT>         * @param b Parameter {@code b}.<a name="line.127"></a>
<FONT color="green">128</FONT>         * @param epsilon When the absolute value of the nth item in the<a name="line.128"></a>
<FONT color="green">129</FONT>         * series is less than epsilon the approximation ceases to calculate<a name="line.129"></a>
<FONT color="green">130</FONT>         * further elements in the series.<a name="line.130"></a>
<FONT color="green">131</FONT>         * @return the regularized beta function I(x, a, b)<a name="line.131"></a>
<FONT color="green">132</FONT>         * @throws org.apache.commons.math3.exception.MaxCountExceededException<a name="line.132"></a>
<FONT color="green">133</FONT>         * if the algorithm fails to converge.<a name="line.133"></a>
<FONT color="green">134</FONT>         */<a name="line.134"></a>
<FONT color="green">135</FONT>        public static double regularizedBeta(double x,<a name="line.135"></a>
<FONT color="green">136</FONT>                                             double a, double b,<a name="line.136"></a>
<FONT color="green">137</FONT>                                             double epsilon) {<a name="line.137"></a>
<FONT color="green">138</FONT>            return regularizedBeta(x, a, b, epsilon, Integer.MAX_VALUE);<a name="line.138"></a>
<FONT color="green">139</FONT>        }<a name="line.139"></a>
<FONT color="green">140</FONT>    <a name="line.140"></a>
<FONT color="green">141</FONT>        /**<a name="line.141"></a>
<FONT color="green">142</FONT>         * Returns the regularized beta function I(x, a, b).<a name="line.142"></a>
<FONT color="green">143</FONT>         *<a name="line.143"></a>
<FONT color="green">144</FONT>         * @param x the value.<a name="line.144"></a>
<FONT color="green">145</FONT>         * @param a Parameter {@code a}.<a name="line.145"></a>
<FONT color="green">146</FONT>         * @param b Parameter {@code b}.<a name="line.146"></a>
<FONT color="green">147</FONT>         * @param maxIterations Maximum number of "iterations" to complete.<a name="line.147"></a>
<FONT color="green">148</FONT>         * @return the regularized beta function I(x, a, b)<a name="line.148"></a>
<FONT color="green">149</FONT>         * @throws org.apache.commons.math3.exception.MaxCountExceededException<a name="line.149"></a>
<FONT color="green">150</FONT>         * if the algorithm fails to converge.<a name="line.150"></a>
<FONT color="green">151</FONT>         */<a name="line.151"></a>
<FONT color="green">152</FONT>        public static double regularizedBeta(double x,<a name="line.152"></a>
<FONT color="green">153</FONT>                                             double a, double b,<a name="line.153"></a>
<FONT color="green">154</FONT>                                             int maxIterations) {<a name="line.154"></a>
<FONT color="green">155</FONT>            return regularizedBeta(x, a, b, DEFAULT_EPSILON, maxIterations);<a name="line.155"></a>
<FONT color="green">156</FONT>        }<a name="line.156"></a>
<FONT color="green">157</FONT>    <a name="line.157"></a>
<FONT color="green">158</FONT>        /**<a name="line.158"></a>
<FONT color="green">159</FONT>         * Returns the regularized beta function I(x, a, b).<a name="line.159"></a>
<FONT color="green">160</FONT>         *<a name="line.160"></a>
<FONT color="green">161</FONT>         * The implementation of this method is based on:<a name="line.161"></a>
<FONT color="green">162</FONT>         * &lt;ul&gt;<a name="line.162"></a>
<FONT color="green">163</FONT>         * &lt;li&gt;<a name="line.163"></a>
<FONT color="green">164</FONT>         * &lt;a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html"&gt;<a name="line.164"></a>
<FONT color="green">165</FONT>         * Regularized Beta Function&lt;/a&gt;.&lt;/li&gt;<a name="line.165"></a>
<FONT color="green">166</FONT>         * &lt;li&gt;<a name="line.166"></a>
<FONT color="green">167</FONT>         * &lt;a href="http://functions.wolfram.com/06.21.10.0001.01"&gt;<a name="line.167"></a>
<FONT color="green">168</FONT>         * Regularized Beta Function&lt;/a&gt;.&lt;/li&gt;<a name="line.168"></a>
<FONT color="green">169</FONT>         * &lt;/ul&gt;<a name="line.169"></a>
<FONT color="green">170</FONT>         *<a name="line.170"></a>
<FONT color="green">171</FONT>         * @param x the value.<a name="line.171"></a>
<FONT color="green">172</FONT>         * @param a Parameter {@code a}.<a name="line.172"></a>
<FONT color="green">173</FONT>         * @param b Parameter {@code b}.<a name="line.173"></a>
<FONT color="green">174</FONT>         * @param epsilon When the absolute value of the nth item in the<a name="line.174"></a>
<FONT color="green">175</FONT>         * series is less than epsilon the approximation ceases to calculate<a name="line.175"></a>
<FONT color="green">176</FONT>         * further elements in the series.<a name="line.176"></a>
<FONT color="green">177</FONT>         * @param maxIterations Maximum number of "iterations" to complete.<a name="line.177"></a>
<FONT color="green">178</FONT>         * @return the regularized beta function I(x, a, b)<a name="line.178"></a>
<FONT color="green">179</FONT>         * @throws org.apache.commons.math3.exception.MaxCountExceededException<a name="line.179"></a>
<FONT color="green">180</FONT>         * if the algorithm fails to converge.<a name="line.180"></a>
<FONT color="green">181</FONT>         */<a name="line.181"></a>
<FONT color="green">182</FONT>        public static double regularizedBeta(double x,<a name="line.182"></a>
<FONT color="green">183</FONT>                                             final double a, final double b,<a name="line.183"></a>
<FONT color="green">184</FONT>                                             double epsilon, int maxIterations) {<a name="line.184"></a>
<FONT color="green">185</FONT>            double ret;<a name="line.185"></a>
<FONT color="green">186</FONT>    <a name="line.186"></a>
<FONT color="green">187</FONT>            if (Double.isNaN(x) ||<a name="line.187"></a>
<FONT color="green">188</FONT>                Double.isNaN(a) ||<a name="line.188"></a>
<FONT color="green">189</FONT>                Double.isNaN(b) ||<a name="line.189"></a>
<FONT color="green">190</FONT>                x &lt; 0 ||<a name="line.190"></a>
<FONT color="green">191</FONT>                x &gt; 1 ||<a name="line.191"></a>
<FONT color="green">192</FONT>                a &lt;= 0.0 ||<a name="line.192"></a>
<FONT color="green">193</FONT>                b &lt;= 0.0) {<a name="line.193"></a>
<FONT color="green">194</FONT>                ret = Double.NaN;<a name="line.194"></a>
<FONT color="green">195</FONT>            } else if (x &gt; (a + 1.0) / (a + b + 2.0)) {<a name="line.195"></a>
<FONT color="green">196</FONT>                ret = 1.0 - regularizedBeta(1.0 - x, b, a, epsilon, maxIterations);<a name="line.196"></a>
<FONT color="green">197</FONT>            } else {<a name="line.197"></a>
<FONT color="green">198</FONT>                ContinuedFraction fraction = new ContinuedFraction() {<a name="line.198"></a>
<FONT color="green">199</FONT>    <a name="line.199"></a>
<FONT color="green">200</FONT>                    @Override<a name="line.200"></a>
<FONT color="green">201</FONT>                    protected double getB(int n, double x) {<a name="line.201"></a>
<FONT color="green">202</FONT>                        double ret;<a name="line.202"></a>
<FONT color="green">203</FONT>                        double m;<a name="line.203"></a>
<FONT color="green">204</FONT>                        if (n % 2 == 0) { // even<a name="line.204"></a>
<FONT color="green">205</FONT>                            m = n / 2.0;<a name="line.205"></a>
<FONT color="green">206</FONT>                            ret = (m * (b - m) * x) /<a name="line.206"></a>
<FONT color="green">207</FONT>                                ((a + (2 * m) - 1) * (a + (2 * m)));<a name="line.207"></a>
<FONT color="green">208</FONT>                        } else {<a name="line.208"></a>
<FONT color="green">209</FONT>                            m = (n - 1.0) / 2.0;<a name="line.209"></a>
<FONT color="green">210</FONT>                            ret = -((a + m) * (a + b + m) * x) /<a name="line.210"></a>
<FONT color="green">211</FONT>                                    ((a + (2 * m)) * (a + (2 * m) + 1.0));<a name="line.211"></a>
<FONT color="green">212</FONT>                        }<a name="line.212"></a>
<FONT color="green">213</FONT>                        return ret;<a name="line.213"></a>
<FONT color="green">214</FONT>                    }<a name="line.214"></a>
<FONT color="green">215</FONT>    <a name="line.215"></a>
<FONT color="green">216</FONT>                    @Override<a name="line.216"></a>
<FONT color="green">217</FONT>                    protected double getA(int n, double x) {<a name="line.217"></a>
<FONT color="green">218</FONT>                        return 1.0;<a name="line.218"></a>
<FONT color="green">219</FONT>                    }<a name="line.219"></a>
<FONT color="green">220</FONT>                };<a name="line.220"></a>
<FONT color="green">221</FONT>                ret = FastMath.exp((a * FastMath.log(x)) + (b * FastMath.log(1.0 - x)) -<a name="line.221"></a>
<FONT color="green">222</FONT>                    FastMath.log(a) - logBeta(a, b)) *<a name="line.222"></a>
<FONT color="green">223</FONT>                    1.0 / fraction.evaluate(x, epsilon, maxIterations);<a name="line.223"></a>
<FONT color="green">224</FONT>            }<a name="line.224"></a>
<FONT color="green">225</FONT>    <a name="line.225"></a>
<FONT color="green">226</FONT>            return ret;<a name="line.226"></a>
<FONT color="green">227</FONT>        }<a name="line.227"></a>
<FONT color="green">228</FONT>    <a name="line.228"></a>
<FONT color="green">229</FONT>        /**<a name="line.229"></a>
<FONT color="green">230</FONT>         * Returns the natural logarithm of the beta function B(a, b).<a name="line.230"></a>
<FONT color="green">231</FONT>         *<a name="line.231"></a>
<FONT color="green">232</FONT>         * The implementation of this method is based on:<a name="line.232"></a>
<FONT color="green">233</FONT>         * &lt;ul&gt;<a name="line.233"></a>
<FONT color="green">234</FONT>         * &lt;li&gt;&lt;a href="http://mathworld.wolfram.com/BetaFunction.html"&gt;<a name="line.234"></a>
<FONT color="green">235</FONT>         * Beta Function&lt;/a&gt;, equation (1).&lt;/li&gt;<a name="line.235"></a>
<FONT color="green">236</FONT>         * &lt;/ul&gt;<a name="line.236"></a>
<FONT color="green">237</FONT>         *<a name="line.237"></a>
<FONT color="green">238</FONT>         * @param a Parameter {@code a}.<a name="line.238"></a>
<FONT color="green">239</FONT>         * @param b Parameter {@code b}.<a name="line.239"></a>
<FONT color="green">240</FONT>         * @param epsilon This parameter is ignored.<a name="line.240"></a>
<FONT color="green">241</FONT>         * @param maxIterations This parameter is ignored.<a name="line.241"></a>
<FONT color="green">242</FONT>         * @return log(B(a, b)).<a name="line.242"></a>
<FONT color="green">243</FONT>         * @deprecated as of version 3.1, this method is deprecated as the<a name="line.243"></a>
<FONT color="green">244</FONT>         * computation of the beta function is no longer iterative; it will be<a name="line.244"></a>
<FONT color="green">245</FONT>         * removed in version 4.0. Current implementation of this method<a name="line.245"></a>
<FONT color="green">246</FONT>         * internally calls {@link #logBeta(double, double)}.<a name="line.246"></a>
<FONT color="green">247</FONT>         */<a name="line.247"></a>
<FONT color="green">248</FONT>        @Deprecated<a name="line.248"></a>
<FONT color="green">249</FONT>        public static double logBeta(double a, double b,<a name="line.249"></a>
<FONT color="green">250</FONT>                                     double epsilon,<a name="line.250"></a>
<FONT color="green">251</FONT>                                     int maxIterations) {<a name="line.251"></a>
<FONT color="green">252</FONT>    <a name="line.252"></a>
<FONT color="green">253</FONT>            return logBeta(a, b);<a name="line.253"></a>
<FONT color="green">254</FONT>        }<a name="line.254"></a>
<FONT color="green">255</FONT>    <a name="line.255"></a>
<FONT color="green">256</FONT>    <a name="line.256"></a>
<FONT color="green">257</FONT>        /**<a name="line.257"></a>
<FONT color="green">258</FONT>         * Returns the value of log Γ(a + b) for 1 ≤ a, b ≤ 2. Based on the<a name="line.258"></a>
<FONT color="green">259</FONT>         * &lt;em&gt;NSWC Library of Mathematics Subroutines&lt;/em&gt; double precision<a name="line.259"></a>
<FONT color="green">260</FONT>         * implementation, {@code DGSMLN}. In {@link BetaTest#testLogGammaSum()},<a name="line.260"></a>
<FONT color="green">261</FONT>         * this private method is accessed through reflection.<a name="line.261"></a>
<FONT color="green">262</FONT>         *<a name="line.262"></a>
<FONT color="green">263</FONT>         * @param a First argument.<a name="line.263"></a>
<FONT color="green">264</FONT>         * @param b Second argument.<a name="line.264"></a>
<FONT color="green">265</FONT>         * @return the value of {@code log(Gamma(a + b))}.<a name="line.265"></a>
<FONT color="green">266</FONT>         * @throws OutOfRangeException if {@code a} or {@code b} is lower than<a name="line.266"></a>
<FONT color="green">267</FONT>         * {@code 1.0} or greater than {@code 2.0}.<a name="line.267"></a>
<FONT color="green">268</FONT>         */<a name="line.268"></a>
<FONT color="green">269</FONT>        private static double logGammaSum(final double a, final double b)<a name="line.269"></a>
<FONT color="green">270</FONT>            throws OutOfRangeException {<a name="line.270"></a>
<FONT color="green">271</FONT>    <a name="line.271"></a>
<FONT color="green">272</FONT>            if ((a &lt; 1.0) || (a &gt; 2.0)) {<a name="line.272"></a>
<FONT color="green">273</FONT>                throw new OutOfRangeException(a, 1.0, 2.0);<a name="line.273"></a>
<FONT color="green">274</FONT>            }<a name="line.274"></a>
<FONT color="green">275</FONT>            if ((b &lt; 1.0) || (b &gt; 2.0)) {<a name="line.275"></a>
<FONT color="green">276</FONT>                throw new OutOfRangeException(b, 1.0, 2.0);<a name="line.276"></a>
<FONT color="green">277</FONT>            }<a name="line.277"></a>
<FONT color="green">278</FONT>    <a name="line.278"></a>
<FONT color="green">279</FONT>            final double x = (a - 1.0) + (b - 1.0);<a name="line.279"></a>
<FONT color="green">280</FONT>            if (x &lt;= 0.5) {<a name="line.280"></a>
<FONT color="green">281</FONT>                return Gamma.logGamma1p(1.0 + x);<a name="line.281"></a>
<FONT color="green">282</FONT>            } else if (x &lt;= 1.5) {<a name="line.282"></a>
<FONT color="green">283</FONT>                return Gamma.logGamma1p(x) + FastMath.log1p(x);<a name="line.283"></a>
<FONT color="green">284</FONT>            } else {<a name="line.284"></a>
<FONT color="green">285</FONT>                return Gamma.logGamma1p(x - 1.0) + FastMath.log(x * (1.0 + x));<a name="line.285"></a>
<FONT color="green">286</FONT>            }<a name="line.286"></a>
<FONT color="green">287</FONT>        }<a name="line.287"></a>
<FONT color="green">288</FONT>    <a name="line.288"></a>
<FONT color="green">289</FONT>        /**<a name="line.289"></a>
<FONT color="green">290</FONT>         * Returns the value of log[Γ(b) / Γ(a + b)] for a ≥ 0 and b ≥ 10. Based on<a name="line.290"></a>
<FONT color="green">291</FONT>         * the &lt;em&gt;NSWC Library of Mathematics Subroutines&lt;/em&gt; double precision<a name="line.291"></a>
<FONT color="green">292</FONT>         * implementation, {@code DLGDIV}. In<a name="line.292"></a>
<FONT color="green">293</FONT>         * {@link BetaTest#testLogGammaMinusLogGammaSum()}, this private method is<a name="line.293"></a>
<FONT color="green">294</FONT>         * accessed through reflection.<a name="line.294"></a>
<FONT color="green">295</FONT>         *<a name="line.295"></a>
<FONT color="green">296</FONT>         * @param a First argument.<a name="line.296"></a>
<FONT color="green">297</FONT>         * @param b Second argument.<a name="line.297"></a>
<FONT color="green">298</FONT>         * @return the value of {@code log(Gamma(b) / Gamma(a + b))}.<a name="line.298"></a>
<FONT color="green">299</FONT>         * @throws NumberIsTooSmallException if {@code a &lt; 0.0} or {@code b &lt; 10.0}.<a name="line.299"></a>
<FONT color="green">300</FONT>         */<a name="line.300"></a>
<FONT color="green">301</FONT>        private static double logGammaMinusLogGammaSum(final double a,<a name="line.301"></a>
<FONT color="green">302</FONT>                                                       final double b)<a name="line.302"></a>
<FONT color="green">303</FONT>            throws NumberIsTooSmallException {<a name="line.303"></a>
<FONT color="green">304</FONT>    <a name="line.304"></a>
<FONT color="green">305</FONT>            if (a &lt; 0.0) {<a name="line.305"></a>
<FONT color="green">306</FONT>                throw new NumberIsTooSmallException(a, 0.0, true);<a name="line.306"></a>
<FONT color="green">307</FONT>            }<a name="line.307"></a>
<FONT color="green">308</FONT>            if (b &lt; 10.0) {<a name="line.308"></a>
<FONT color="green">309</FONT>                throw new NumberIsTooSmallException(b, 10.0, true);<a name="line.309"></a>
<FONT color="green">310</FONT>            }<a name="line.310"></a>
<FONT color="green">311</FONT>    <a name="line.311"></a>
<FONT color="green">312</FONT>            /*<a name="line.312"></a>
<FONT color="green">313</FONT>             * d = a + b - 0.5<a name="line.313"></a>
<FONT color="green">314</FONT>             */<a name="line.314"></a>
<FONT color="green">315</FONT>            final double d;<a name="line.315"></a>
<FONT color="green">316</FONT>            final double w;<a name="line.316"></a>
<FONT color="green">317</FONT>            if (a &lt;= b) {<a name="line.317"></a>
<FONT color="green">318</FONT>                d = b + (a - 0.5);<a name="line.318"></a>
<FONT color="green">319</FONT>                w = deltaMinusDeltaSum(a, b);<a name="line.319"></a>
<FONT color="green">320</FONT>            } else {<a name="line.320"></a>
<FONT color="green">321</FONT>                d = a + (b - 0.5);<a name="line.321"></a>
<FONT color="green">322</FONT>                w = deltaMinusDeltaSum(b, a);<a name="line.322"></a>
<FONT color="green">323</FONT>            }<a name="line.323"></a>
<FONT color="green">324</FONT>    <a name="line.324"></a>
<FONT color="green">325</FONT>            final double u = d * FastMath.log1p(a / b);<a name="line.325"></a>
<FONT color="green">326</FONT>            final double v = a * (FastMath.log(b) - 1.0);<a name="line.326"></a>
<FONT color="green">327</FONT>    <a name="line.327"></a>
<FONT color="green">328</FONT>            return u &lt;= v ? (w - u) - v : (w - v) - u;<a name="line.328"></a>
<FONT color="green">329</FONT>        }<a name="line.329"></a>
<FONT color="green">330</FONT>    <a name="line.330"></a>
<FONT color="green">331</FONT>        /**<a name="line.331"></a>
<FONT color="green">332</FONT>         * Returns the value of Δ(b) - Δ(a + b), with 0 ≤ a ≤ b and b ≥ 10. Based<a name="line.332"></a>
<FONT color="green">333</FONT>         * on equations (26), (27) and (28) in Didonato and Morris (1992).<a name="line.333"></a>
<FONT color="green">334</FONT>         *<a name="line.334"></a>
<FONT color="green">335</FONT>         * @param a First argument.<a name="line.335"></a>
<FONT color="green">336</FONT>         * @param b Second argument.<a name="line.336"></a>
<FONT color="green">337</FONT>         * @return the value of {@code Delta(b) - Delta(a + b)}<a name="line.337"></a>
<FONT color="green">338</FONT>         * @throws OutOfRangeException if {@code a &lt; 0} or {@code a &gt; b}<a name="line.338"></a>
<FONT color="green">339</FONT>         * @throws NumberIsTooSmallException if {@code b &lt; 10}<a name="line.339"></a>
<FONT color="green">340</FONT>         */<a name="line.340"></a>
<FONT color="green">341</FONT>        private static double deltaMinusDeltaSum(final double a,<a name="line.341"></a>
<FONT color="green">342</FONT>                                                 final double b)<a name="line.342"></a>
<FONT color="green">343</FONT>            throws OutOfRangeException, NumberIsTooSmallException {<a name="line.343"></a>
<FONT color="green">344</FONT>    <a name="line.344"></a>
<FONT color="green">345</FONT>            if ((a &lt; 0) || (a &gt; b)) {<a name="line.345"></a>
<FONT color="green">346</FONT>                throw new OutOfRangeException(a, 0, b);<a name="line.346"></a>
<FONT color="green">347</FONT>            }<a name="line.347"></a>
<FONT color="green">348</FONT>            if (b &lt; 10) {<a name="line.348"></a>
<FONT color="green">349</FONT>                throw new NumberIsTooSmallException(b, 10, true);<a name="line.349"></a>
<FONT color="green">350</FONT>            }<a name="line.350"></a>
<FONT color="green">351</FONT>    <a name="line.351"></a>
<FONT color="green">352</FONT>            final double h = a / b;<a name="line.352"></a>
<FONT color="green">353</FONT>            final double p = h / (1.0 + h);<a name="line.353"></a>
<FONT color="green">354</FONT>            final double q = 1.0 / (1.0 + h);<a name="line.354"></a>
<FONT color="green">355</FONT>            final double q2 = q * q;<a name="line.355"></a>
<FONT color="green">356</FONT>            /*<a name="line.356"></a>
<FONT color="green">357</FONT>             * s[i] = 1 + q + ... - q**(2 * i)<a name="line.357"></a>
<FONT color="green">358</FONT>             */<a name="line.358"></a>
<FONT color="green">359</FONT>            final double[] s = new double[DELTA.length];<a name="line.359"></a>
<FONT color="green">360</FONT>            s[0] = 1.0;<a name="line.360"></a>
<FONT color="green">361</FONT>            for (int i = 1; i &lt; s.length; i++) {<a name="line.361"></a>
<FONT color="green">362</FONT>                s[i] = 1.0 + (q + q2 * s[i - 1]);<a name="line.362"></a>
<FONT color="green">363</FONT>            }<a name="line.363"></a>
<FONT color="green">364</FONT>            /*<a name="line.364"></a>
<FONT color="green">365</FONT>             * w = Delta(b) - Delta(a + b)<a name="line.365"></a>
<FONT color="green">366</FONT>             */<a name="line.366"></a>
<FONT color="green">367</FONT>            final double sqrtT = 10.0 / b;<a name="line.367"></a>
<FONT color="green">368</FONT>            final double t = sqrtT * sqrtT;<a name="line.368"></a>
<FONT color="green">369</FONT>            double w = DELTA[DELTA.length - 1] * s[s.length - 1];<a name="line.369"></a>
<FONT color="green">370</FONT>            for (int i = DELTA.length - 2; i &gt;= 0; i--) {<a name="line.370"></a>
<FONT color="green">371</FONT>                w = t * w + DELTA[i] * s[i];<a name="line.371"></a>
<FONT color="green">372</FONT>            }<a name="line.372"></a>
<FONT color="green">373</FONT>            return w * p / b;<a name="line.373"></a>
<FONT color="green">374</FONT>        }<a name="line.374"></a>
<FONT color="green">375</FONT>    <a name="line.375"></a>
<FONT color="green">376</FONT>        /**<a name="line.376"></a>
<FONT color="green">377</FONT>         * Returns the value of Δ(p) + Δ(q) - Δ(p + q), with p, q ≥ 10. Based on<a name="line.377"></a>
<FONT color="green">378</FONT>         * the &lt;em&gt;NSWC Library of Mathematics Subroutines&lt;/em&gt; double precision<a name="line.378"></a>
<FONT color="green">379</FONT>         * implementation, {@code DBCORR}. In<a name="line.379"></a>
<FONT color="green">380</FONT>         * {@link BetaTest#testSumDeltaMinusDeltaSum()}, this private method is<a name="line.380"></a>
<FONT color="green">381</FONT>         * accessed through reflection.<a name="line.381"></a>
<FONT color="green">382</FONT>         *<a name="line.382"></a>
<FONT color="green">383</FONT>         * @param p First argument.<a name="line.383"></a>
<FONT color="green">384</FONT>         * @param q Second argument.<a name="line.384"></a>
<FONT color="green">385</FONT>         * @return the value of {@code Delta(p) + Delta(q) - Delta(p + q)}.<a name="line.385"></a>
<FONT color="green">386</FONT>         * @throws NumberIsTooSmallException if {@code p &lt; 10.0} or {@code q &lt; 10.0}.<a name="line.386"></a>
<FONT color="green">387</FONT>         */<a name="line.387"></a>
<FONT color="green">388</FONT>        private static double sumDeltaMinusDeltaSum(final double p,<a name="line.388"></a>
<FONT color="green">389</FONT>                                                    final double q) {<a name="line.389"></a>
<FONT color="green">390</FONT>    <a name="line.390"></a>
<FONT color="green">391</FONT>            if (p &lt; 10.0) {<a name="line.391"></a>
<FONT color="green">392</FONT>                throw new NumberIsTooSmallException(p, 10.0, true);<a name="line.392"></a>
<FONT color="green">393</FONT>            }<a name="line.393"></a>
<FONT color="green">394</FONT>            if (q &lt; 10.0) {<a name="line.394"></a>
<FONT color="green">395</FONT>                throw new NumberIsTooSmallException(q, 10.0, true);<a name="line.395"></a>
<FONT color="green">396</FONT>            }<a name="line.396"></a>
<FONT color="green">397</FONT>    <a name="line.397"></a>
<FONT color="green">398</FONT>            final double a = FastMath.min(p, q);<a name="line.398"></a>
<FONT color="green">399</FONT>            final double b = FastMath.max(p, q);<a name="line.399"></a>
<FONT color="green">400</FONT>            final double sqrtT = 10.0 / a;<a name="line.400"></a>
<FONT color="green">401</FONT>            final double t = sqrtT * sqrtT;<a name="line.401"></a>
<FONT color="green">402</FONT>            double z = DELTA[DELTA.length - 1];<a name="line.402"></a>
<FONT color="green">403</FONT>            for (int i = DELTA.length - 2; i &gt;= 0; i--) {<a name="line.403"></a>
<FONT color="green">404</FONT>                z = t * z + DELTA[i];<a name="line.404"></a>
<FONT color="green">405</FONT>            }<a name="line.405"></a>
<FONT color="green">406</FONT>            return z / a + deltaMinusDeltaSum(a, b);<a name="line.406"></a>
<FONT color="green">407</FONT>        }<a name="line.407"></a>
<FONT color="green">408</FONT>    <a name="line.408"></a>
<FONT color="green">409</FONT>        /**<a name="line.409"></a>
<FONT color="green">410</FONT>         * Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q &gt; 0. Based on the<a name="line.410"></a>
<FONT color="green">411</FONT>         * &lt;em&gt;NSWC Library of Mathematics Subroutines&lt;/em&gt; implementation,<a name="line.411"></a>
<FONT color="green">412</FONT>         * {@code DBETLN}.<a name="line.412"></a>
<FONT color="green">413</FONT>         *<a name="line.413"></a>
<FONT color="green">414</FONT>         * @param p First argument.<a name="line.414"></a>
<FONT color="green">415</FONT>         * @param q Second argument.<a name="line.415"></a>
<FONT color="green">416</FONT>         * @return the value of {@code log(Beta(p, q))}, {@code NaN} if<a name="line.416"></a>
<FONT color="green">417</FONT>         * {@code p &lt;= 0} or {@code q &lt;= 0}.<a name="line.417"></a>
<FONT color="green">418</FONT>         */<a name="line.418"></a>
<FONT color="green">419</FONT>        public static double logBeta(final double p, final double q) {<a name="line.419"></a>
<FONT color="green">420</FONT>            if (Double.isNaN(p) || Double.isNaN(q) || (p &lt;= 0.0) || (q &lt;= 0.0)) {<a name="line.420"></a>
<FONT color="green">421</FONT>                return Double.NaN;<a name="line.421"></a>
<FONT color="green">422</FONT>            }<a name="line.422"></a>
<FONT color="green">423</FONT>    <a name="line.423"></a>
<FONT color="green">424</FONT>            final double a = FastMath.min(p, q);<a name="line.424"></a>
<FONT color="green">425</FONT>            final double b = FastMath.max(p, q);<a name="line.425"></a>
<FONT color="green">426</FONT>            if (a &gt;= 10.0) {<a name="line.426"></a>
<FONT color="green">427</FONT>                final double w = sumDeltaMinusDeltaSum(a, b);<a name="line.427"></a>
<FONT color="green">428</FONT>                final double h = a / b;<a name="line.428"></a>
<FONT color="green">429</FONT>                final double c = h / (1.0 + h);<a name="line.429"></a>
<FONT color="green">430</FONT>                final double u = -(a - 0.5) * FastMath.log(c);<a name="line.430"></a>
<FONT color="green">431</FONT>                final double v = b * FastMath.log1p(h);<a name="line.431"></a>
<FONT color="green">432</FONT>                if (u &lt;= v) {<a name="line.432"></a>
<FONT color="green">433</FONT>                    return (((-0.5 * FastMath.log(b) + HALF_LOG_TWO_PI) + w) - u) - v;<a name="line.433"></a>
<FONT color="green">434</FONT>                } else {<a name="line.434"></a>
<FONT color="green">435</FONT>                    return (((-0.5 * FastMath.log(b) + HALF_LOG_TWO_PI) + w) - v) - u;<a name="line.435"></a>
<FONT color="green">436</FONT>                }<a name="line.436"></a>
<FONT color="green">437</FONT>            } else if (a &gt; 2.0) {<a name="line.437"></a>
<FONT color="green">438</FONT>                if (b &gt; 1000.0) {<a name="line.438"></a>
<FONT color="green">439</FONT>                    final int n = (int) FastMath.floor(a - 1.0);<a name="line.439"></a>
<FONT color="green">440</FONT>                    double prod = 1.0;<a name="line.440"></a>
<FONT color="green">441</FONT>                    double ared = a;<a name="line.441"></a>
<FONT color="green">442</FONT>                    for (int i = 0; i &lt; n; i++) {<a name="line.442"></a>
<FONT color="green">443</FONT>                        ared -= 1.0;<a name="line.443"></a>
<FONT color="green">444</FONT>                        prod *= ared / (1.0 + ared / b);<a name="line.444"></a>
<FONT color="green">445</FONT>                    }<a name="line.445"></a>
<FONT color="green">446</FONT>                    return (FastMath.log(prod) - n * FastMath.log(b)) +<a name="line.446"></a>
<FONT color="green">447</FONT>                            (Gamma.logGamma(ared) +<a name="line.447"></a>
<FONT color="green">448</FONT>                             logGammaMinusLogGammaSum(ared, b));<a name="line.448"></a>
<FONT color="green">449</FONT>                } else {<a name="line.449"></a>
<FONT color="green">450</FONT>                    double prod1 = 1.0;<a name="line.450"></a>
<FONT color="green">451</FONT>                    double ared = a;<a name="line.451"></a>
<FONT color="green">452</FONT>                    while (ared &gt; 2.0) {<a name="line.452"></a>
<FONT color="green">453</FONT>                        ared -= 1.0;<a name="line.453"></a>
<FONT color="green">454</FONT>                        final double h = ared / b;<a name="line.454"></a>
<FONT color="green">455</FONT>                        prod1 *= h / (1.0 + h);<a name="line.455"></a>
<FONT color="green">456</FONT>                    }<a name="line.456"></a>
<FONT color="green">457</FONT>                    if (b &lt; 10.0) {<a name="line.457"></a>
<FONT color="green">458</FONT>                        double prod2 = 1.0;<a name="line.458"></a>
<FONT color="green">459</FONT>                        double bred = b;<a name="line.459"></a>
<FONT color="green">460</FONT>                        while (bred &gt; 2.0) {<a name="line.460"></a>
<FONT color="green">461</FONT>                            bred -= 1.0;<a name="line.461"></a>
<FONT color="green">462</FONT>                            prod2 *= bred / (ared + bred);<a name="line.462"></a>
<FONT color="green">463</FONT>                        }<a name="line.463"></a>
<FONT color="green">464</FONT>                        return FastMath.log(prod1) +<a name="line.464"></a>
<FONT color="green">465</FONT>                               FastMath.log(prod2) +<a name="line.465"></a>
<FONT color="green">466</FONT>                               (Gamma.logGamma(ared) +<a name="line.466"></a>
<FONT color="green">467</FONT>                               (Gamma.logGamma(bred) -<a name="line.467"></a>
<FONT color="green">468</FONT>                                logGammaSum(ared, bred)));<a name="line.468"></a>
<FONT color="green">469</FONT>                    } else {<a name="line.469"></a>
<FONT color="green">470</FONT>                        return FastMath.log(prod1) +<a name="line.470"></a>
<FONT color="green">471</FONT>                               Gamma.logGamma(ared) +<a name="line.471"></a>
<FONT color="green">472</FONT>                               logGammaMinusLogGammaSum(ared, b);<a name="line.472"></a>
<FONT color="green">473</FONT>                    }<a name="line.473"></a>
<FONT color="green">474</FONT>                }<a name="line.474"></a>
<FONT color="green">475</FONT>            } else if (a &gt;= 1.0) {<a name="line.475"></a>
<FONT color="green">476</FONT>                if (b &gt; 2.0) {<a name="line.476"></a>
<FONT color="green">477</FONT>                    if (b &lt; 10.0) {<a name="line.477"></a>
<FONT color="green">478</FONT>                        double prod = 1.0;<a name="line.478"></a>
<FONT color="green">479</FONT>                        double bred = b;<a name="line.479"></a>
<FONT color="green">480</FONT>                        while (bred &gt; 2.0) {<a name="line.480"></a>
<FONT color="green">481</FONT>                            bred -= 1.0;<a name="line.481"></a>
<FONT color="green">482</FONT>                            prod *= bred / (a + bred);<a name="line.482"></a>
<FONT color="green">483</FONT>                        }<a name="line.483"></a>
<FONT color="green">484</FONT>                        return FastMath.log(prod) +<a name="line.484"></a>
<FONT color="green">485</FONT>                               (Gamma.logGamma(a) +<a name="line.485"></a>
<FONT color="green">486</FONT>                                (Gamma.logGamma(bred) -<a name="line.486"></a>
<FONT color="green">487</FONT>                                 logGammaSum(a, bred)));<a name="line.487"></a>
<FONT color="green">488</FONT>                    } else {<a name="line.488"></a>
<FONT color="green">489</FONT>                        return Gamma.logGamma(a) +<a name="line.489"></a>
<FONT color="green">490</FONT>                               logGammaMinusLogGammaSum(a, b);<a name="line.490"></a>
<FONT color="green">491</FONT>                    }<a name="line.491"></a>
<FONT color="green">492</FONT>                } else {<a name="line.492"></a>
<FONT color="green">493</FONT>                    return Gamma.logGamma(a) +<a name="line.493"></a>
<FONT color="green">494</FONT>                           Gamma.logGamma(b) -<a name="line.494"></a>
<FONT color="green">495</FONT>                           logGammaSum(a, b);<a name="line.495"></a>
<FONT color="green">496</FONT>                }<a name="line.496"></a>
<FONT color="green">497</FONT>            } else {<a name="line.497"></a>
<FONT color="green">498</FONT>                if (b &gt;= 10.0) {<a name="line.498"></a>
<FONT color="green">499</FONT>                    return Gamma.logGamma(a) +<a name="line.499"></a>
<FONT color="green">500</FONT>                           logGammaMinusLogGammaSum(a, b);<a name="line.500"></a>
<FONT color="green">501</FONT>                } else {<a name="line.501"></a>
<FONT color="green">502</FONT>                    // The following command is the original NSWC implementation.<a name="line.502"></a>
<FONT color="green">503</FONT>                    // return Gamma.logGamma(a) +<a name="line.503"></a>
<FONT color="green">504</FONT>                    // (Gamma.logGamma(b) - Gamma.logGamma(a + b));<a name="line.504"></a>
<FONT color="green">505</FONT>                    // The following command turns out to be more accurate.<a name="line.505"></a>
<FONT color="green">506</FONT>                    return FastMath.log(Gamma.gamma(a) * Gamma.gamma(b) /<a name="line.506"></a>
<FONT color="green">507</FONT>                                        Gamma.gamma(a + b));<a name="line.507"></a>
<FONT color="green">508</FONT>                }<a name="line.508"></a>
<FONT color="green">509</FONT>            }<a name="line.509"></a>
<FONT color="green">510</FONT>        }<a name="line.510"></a>
<FONT color="green">511</FONT>    }<a name="line.511"></a>




























































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